Question 1206591
.
If 1/x - 1/y = 1/(x+y), find (y/x + x/y).
~~~~~~~~~~~~~~~~~~~~~~



        I think that the correct formulation is  DIFFERENT.


        It should be

<pre>
            If 1/x - 1/y = 1/(x+y), find (y/x - x/y).
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will solve it below in this formulation.



<pre>
From 

   {{{1/x}}} - {{{1/y}}} = {{{1/(x+y)}}}    (1)

you get

   {{{(y-x)/(xy)}}} = {{{1/(x+y)}}},

   (y-x)*(y+x) = xy,

    y^2 - x^2 = xy.


Divide both sides by xy

    {{{y/x}}} - {{{x/y)}}} = 1.


At this point, the solution to the problem is complete.


<U>ANSWER</U>.  If  {{{1/x}}} - {{{1/y}}} = {{{1/(x+y)}}},  then  {{{y/x}}} - {{{x/y}}} = 1.
</pre>

Solved.